"Why does the car turn when you turn the steering wheel?" ... Elucidation of the actual situation of the process.

The pleasure of enjoying driving is simply in terms of speed and acceleration, but I think the highlight is the sense of unity between humans and horses when cornering.That is why many readers are also interested in tuning the suspension and body rigidity.However, in the process of a car turning a corner, complicated elements are intertwined in terms of automobile engineering and dynamic sensitivity, and it is not so easy to find a silver bullet to improve performance.Suffice it to say, the most important thing is the basic layout of the car (especially the setting of the center of gravity), but that is the privilege of the designer only.In terms of tuning mass-produced cars, I think the best choice is to first identify a car with a good basic design.On top of that, it can be said that the correct tuning method is to season it according to your own sensibility or to improve the degree of perfection.
As basic knowledge for that, this time, I will focus on the performance of "turning", which is the basis of cornering.


How to turn a car at low speed

Everyone casually drives, steers, and bends the car, but when asked "Why does the car turn?", "When you turn the steering wheel, the direction of the tires turns. I think many people say, "The car will move in that direction."That's right.However, it is very slow, for example when entering the garage, and generally speaking, just turning the steering does not turn the car as intended.This is because centrifugal force is generated due to turning.So, I will talk about that step by step, but first of all, although it is an exceptional situation, let's look at how to bend when centrifugal force does not work. (Since the explanation will be complicated, we will basically use the "two-wheel model" as a diagram. It is assumed that the tread is an extremely narrow car.)

Imagine it in your head.There is one car here, either left or right, but with the steering stationary.Depress the accelerator a little to generate traction.Then the car starts to move little by little and turns in the direction of the front tires. If there is a vector of force that overcomes the rolling resistance of the four wheels, it will naturally move in that direction.If the steering angle is maintained, the car will start turning as it is, and the sum of the front wheel force vector direction and the rear wheel force vector direction will be the force vector in the direction of the red arrow as shown in the figure. The car moves.

In this way, at very low speeds, the centrifugal force is as close to zero as possible, and there is no need to generate a cornering force for the four wheels that balances it.Therefore, as a result, it revolves while rotating according to the angle at which the steering is turned. I think it is easier to understand if you think of it as a "geometry" problem rather than a "motion" problem.
As a reminder, the center of rotation of the vehicle is determined by the steering angle of the front wheels and the wheelbase.
As you can see from the drawing, L (wheelbase) = R (front wheel position turning radius) X sin θ (front wheel steering angle).
R (front wheel position turning radius) = L (wheelbase) / sinθ (front wheel steering angle).

How to bend at the speed at which centrifugal force works

Next, let's think about how to bend at a speed affected by centrifugal force (about XNUMX km / h or more).In this state, the speed of the car is high, so the front tires given the steering angle not only roll in the direction of rotation, but are also pushed out in the direction of travel of the car, and the ground contact surface rubs against the road surface. It will be twisted tightly and the ground plane will bend.This is continuously twisted and then separated repeatedly.As a result, the direction of travel of the tire shifts outward with respect to the direction of rotation of the tire.This offset angle is the slip angle (β).

Here, the force generated by elastic deformation of the cord or rubber twisted at the ground contact part of the tire is called the cornering force in the direction perpendicular to the traveling direction of the tire and the lateral force in the direction perpendicular to the rotation direction of the tire. I'm out.The direction of the force is different by the slip angle between the cornering force and the lateral force. (In this way, it is necessary to distinguish between cornering force and lateral force, but the slip angle is usually within a few degrees, so the magnitude of the force is almost the same.) This force is the centripetal force toward the vehicle body. The theory is that it works and can counteract the centrifugal force at that speed.As a reference, I will introduce a method that can actually verify the occurrence of slip angle.

First, turn at a low speed of XNUMXkm / h or less.It is in a state where a constant turning radius is maintained.Then, gradually accelerate until the vehicle speed exceeds XNUMXkm / h.At this time, at the same rudder angle as the low speed of XNUMXkm / h or less, the car draws a line and swells outward.This is because the direction of travel of the car is shifted outward by the slip angle. (As I will explain later, this is the case of an understeer car.) The figure on the right assumes that the vehicle has moved to point b by increasing the vehicle speed from point a, but the point b is moved to the turning angle of point a. Looking back, it shows that the turning radius is larger.Therefore, in a turning motion where centrifugal force works, if you want to maintain the original turning radius, you need to turn the steering to get the cornering force by the amount of the red arrow.In other words, at the same rudder angle, the slip angle can be recognized by swelling without bending at the radius at low speed.


How to make a steady circular turn

Next, let's take a closer look at the cornering conditions where centrifugal force works.When a slip angle is created on the front wheels and the car body begins to turn, a slip angle is also generated on the rear tires (because the rear wheels are integrated with the car body), and cornering force is generated on both sides.When the cornering force of the front and rear wheels and the centrifugal force acting on each wheel are balanced, it leads to the phenomenon that the car body bends in an arc with a certain radius.In order for a car to turn, it is important that both front and rear wheels have slip angles and that cornering force is generated on the tires.It is easy to think that the turning motion is a factor only for the steering wheel, but the total cornering force of the four wheels, which is the sum of the front wheels and the rear wheels, performs the turning motion while balancing with the centrifugal force.

To explain this from another point of view, the cornering force generated on the front wheels acts as a yaw moment (force that rotates around the Z axis) that rotates inward with respect to the center of gravity of the vehicle.Therefore, the rear wheel side across the center of gravity will rotate outward, and the rear wheel will also have a slip angle, generating a cornering force.However, since the cornering force of the front and rear wheels is a reverse moment, the yaw moment disappears when it is balanced, and it revolves along the circumference with a certain radius while maintaining the yaw rate (rotation speed) at that time. Will be.Such a state is called a steady circular turn.Whether or not to turn quickly when the yaw moment works was previously determined.§ 9It is determined by the magnitude of the yaw moment of inertia mentioned in.
I= M, soThe relationship is = M / I. (I: Yaw moment of inertia M: Yaw moment　: Yaw angular acceleration)
I don't think you will experience this steady circular turn in everyday driving, but if you break down the actual corners, you can see that they connect parts of the circumference of various radii.In actual cornering, movements such as acceleration / deceleration and turning left and right are added to this, and how the car responds to those changes may be the point for dynamic sensitivity.

How to turn in an accelerated circular turn

Now, next is the acceleration circle turn.The theme is how the car turns when the speed is increased while maintaining the steering angle from the state of steady circular rotation, so-called steering characteristics.From the conclusion, "understeer" where the turning radius increases as the vehicle speed increases, "oversteer" where the turning radius decreases, and "neutral steering" where the turning radius does not change even if the vehicle speed changes. There are three types of characteristics as the basic character of each car.

So why does such a difference occur?The following is a fairly technical theory, but I will explain it as simply as possible so that you can get a rough idea of ​​it.
What is important here is the balance of the cornering power (CP) of each wheel. It is called "Neutral Steer Point (NSP)".In general passenger cars, tires of the same size are often selected for the four wheels, and the NSP is located near the center point of the wheelbase on the X axis.And the steering characteristics are determined by the positional relationship between this NSP and the center of gravity (CG).
(Cornering power: Cornering force unit per 1 ° slip angle is [N / Deg])
The figure shows a vehicle with heavy front wheels (typical front-wheel drive). The position of CG is in front of NSP.

Centrifugal force is generated at the center of gravity, so when accelerating, the distance δ between the NSP and the center of gravity and the centrifugal force act as a moment in the opposite direction to the direction in which the bending is about to occur, and the cornering force of the front wheels becomes unbalanced. , It becomes understeer that the turning radius swells.In short, in order to maintain the turning radius when the steering angle is insufficient (under), it is necessary to increase the cornering force by turning the steering and giving more slip angle.
On the other hand, if the CG is behind the NSP, it will be oversteer.Similarly, when accelerating, centrifugal force acts on the center of gravity, so it cannot be balanced with the cornering force of the rear wheels, and the rear wheels will be swung out.As a result, the cornering force of the front wheels is superior to that of the rear wheels, that is, the steering angle is too large (over), so return the steering angle a little (in extreme cases, hit the counter) and reduce the cornering force. Therefore, it is necessary to balance with the rear wheels.In addition, Neutral Steer can maintain the same turning radius even in accelerated turning with the center of gravity and NSP matching.The important thing here is to match the NSP to the CG in order to accelerate and turn the car with understeer and oversteer characteristics.To do so, the difference is whether to increase or decrease the steering angle.In neutral steer, the CG and NSP match at the initial rudder angle.

For reference, the above figure shows these relationships in a slightly more engineering manner. When δ = XNUMX, the numerator of the equation becomes XNUMX, and as a typical example, if a, b and Kf, Kr have the same value, δ = XNUMX.In other words, when the center of gravity is in the center of the vehicle at XNUMX:XNUMX and the cornering power of the front and rear tires is the same, the CG and NSP are at the same point. In the case of δ≻XNUMX, as shown in the figure, when the center of gravity CG is in front of the NSP, the value of a becomes small, so the value of [aKf-bKr] of the numerator becomes a negative value, and δ is positive. It becomes a value (because the expression is a negative value) and understeer.In the case of oversteer, on the contrary, the value of [aKf-bKr] is positive and δ is negative.

What is a comfortable way to bend?

This time, it is a theme that can be said to be the basis for the maneuverability of a car, so there are many explanations about automobile engineering.In discussing the original dynamic Kansei engineering, there are still important factors such as weight transfer by turning, roll rigidity, tire characteristics, etc., but I will talk about them from the next time onwards, but for the time being, it is related to yaw. Let's summarize the factors that influence the dynamic sensitivity in.A sense of unity between a human and a horse, a sense of unity with a car that can be felt as an extension of one's own body ... If you want that kind of comfort in "how to turn a car," what is the problem?
One of them is steering characteristics.It seems that neutral steer is the best in terms of engineering, but it is not in terms of sensitivity.It is generally said, but I think it is safer and more comfortable to turn while correcting the moderately weak under characteristics with the steering.It is not possible to change the basic characteristics when tuning a mass-produced car, but it may be possible to ask for some changes by selecting tires.

Next is the speed of turning with respect to steering operation.Basically, the magnitude of the angular acceleration due to the yaw moment has an effect, which is governed by the moment of inertia peculiar to the vehicle, as described in the text, but it is sensuous due to the rigidity of the steering system and the gear ratio. There is also an effect, so in that sense some tuning will be possible.If the angular acceleration is fast, the direction will change quickly when the steering is turned, and you will feel that the handling is sharp as a sensibility.
Another factor that affects the handling sensation is the yaw angle natural frequency.This is also the engineering performance peculiar to the car, but if you understand it sensuously, the image is as follows.It's dangerous to actually try it, so just imagine it in a virtual world.
When you are going straight at a constant speed in a large safe open space, steer the steering by about 0.7 ° and release your hand.The vehicle speed remains the same.Then, the car will be shaken from side to side and will be in a vibrating state.Eventually, the vibration attenuates, converges, and returns to straight running again.This phenomenon of swinging from side to side is the natural vibration of the yaw angle.The frequency is said to be about 1.2 to XNUMXHz.A high frequency means that the stroke is short, the yaw angular velocity is high, the yaw angular acceleration is high, and in a car, the turning ability is agile and sharp handling characteristics can be obtained.To put it plainly, it is easy to change the direction when turning the steering wheel and easy to return.
I don't think you need to understand the natural frequency in more detail, but for reference, I'll show you a pseudo-experimental model.

Imagine fixing the top of a wire and hanging a ΦXNUMX rebar horizontally at its tip.For example, twist it slightly clockwise (add a rudder) and let go.The rebar turns to the left, then stops at some point and starts to turn to the right.This will be repeated several times. The yaw angle natural frequency is how many times it swings per second.Next, hang a thin and light rebar of the same length, ΦXNUMX, and twist it in the same way to separate it.This time, the swing frequency becomes faster.Since the weights of the two are different, the lighter the weight, the smaller the yaw moment of inertia, and the faster the frequency.In this experiment, the wire, reinforcing bar, and twisting force correspond to the CP of the tire for the wire, the moment of inertia for the reinforcing bar, and the slip angle for the twisting force when returned to the car.

As mentioned above, there is a lot of theory this time as well, but if you search each keyword on the net, you will find many explanations.If you find something difficult to understand, select a site that you can trust and refer to it.
Other engineering issues related to cornering, such as roll stiffness, will be discussed next time.Please continue to read it and make use of it.